283 
direction, which causes the point a, y,z to get at the place RRM 2 3 
v=el te, Y=y(l +8), =-z(4+ 7). Then we may inquire 
into the tensions which occur in a new deformation, and also into 
the increase of energy that takes place then. 
I have carried out this calculation for two special cases. 
If the said dilatations are followed by a shear 
mdr CE TEEN AA oe 
then : 
k 3 dg 
Klat 
A a a 3 
gpd =pdr+—|ull—-{—B+ yy) + 
+ (aren Z)etern—2t Mela. @ 
In y, the terms are comprised which are independent of ¢. We 
may also write: 
: 3 Ed 
Ki u kg ee beant =i 
5 D 3 
+(2+3u—F)e+e ine. 
If, however, after the same dilatations «, 8, y we apply the shear 
e in such a way that the new change of position of the particles is 
expressed by : 
Cy 
a hele aa vissies ml Jeka Li fey" (Rs) 
we find other values, namely : 
e At ASG Rites it) ks 
girmgoar + [ut (Gtp ern (p45, )a|e-© 
5 NED B+8 
Se efu(i—$—29 7) 4 (argent |© 
We see that in this case Y. cannot be obtained by differentiating 
p with respect to €, as in the preceding one. 
As third application we calculate, accurate down to £°, the tensions 
which occur when a body is deformed out of its natural position 
according to the equations : 
vr hez yoy EZ. 
We then find: 
